Article
Engineering, Multidisciplinary
Junpu Li, Lan Zhang, Qinghua Qin
Summary: The article applies the singular boundary method to efficiently calculate electromagnetic scattering from complex targets, introduces a regularized fast multipole method, uses specific basis functions and modified fundamental solutions to address key issues in simulation, and reduces computational errors by introducing a preconditioner and origin intensity factor.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Engineering, Multidisciplinary
Junpu Li, Lan Zhang
Summary: This study applies the latest research results based on the semi-analytical boundary collocation method to calculate computational electromagnetics, addressing common mechanical bottlenecks encountered in simulating electromagnetic scattering and introducing new methods to improve computational efficiency and accuracy.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Engineering, Multidisciplinary
Javad Fakhraei, Robert Arcos, Teresa Pamies, Jordi Romeu
Summary: In this paper, a numerical methodology based on a 2.5D singular boundary method (SBM) is proposed and studied for acoustic radiation and scattering problems. The feasibility, validity, and accuracy of the proposed method are demonstrated through comparisons with other methods and analytical solutions. The study finds that the proposed method achieves higher numerical accuracy and is simpler and more robust for complex geometries compared to other methods.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Mathematics, Applied
Junpu Li, Lan Zhang, Shouyu Cai, Na Li
Summary: This research proposes a regularized singular boundary method for quickly calculating the singularity of the special Green's function at origin. By utilizing the special Green's function and the origin intensity factor technique, an explicit intensity factor suitable for three-dimensional ocean dynamics is derived. The method does not involve singular integrals, resulting in improved computational efficiency and accuracy.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Thermodynamics
Junpu Li, Lan Zhang, Qinghua Qin, Fei Wang
Summary: This paper proposes a novel localized spatiotemporal particle collocation method (LSPCM) for analyzing long-time transient homogeneous diffusion problems. By bypassing traditional mathematical transformation methods, this method can directly approximate diffusion problems and also has a simplified linear system solving process.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2022)
Article
Engineering, Multidisciplinary
Q. G. Liu, C. M. Fan, B. Sarler
Summary: The paper introduces a Localized Method of Fundamental Solutions (LMFS) for solving two-dimensional anisotropic elasticity problems by dividing the computational domain into overlapping subdomains and combining the classical Method of Fundamental Solutions (MFS) to achieve expression and calculation of the solution.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Review
Engineering, Multidisciplinary
Zhuojia Fu, Qiang Xi, Yan Gu, Junpu Li, Wenzhen Qu, Linlin Sun, Xing Wei, Fajie Wang, Ji Lin, Weiwei Li, Wenzhi Xu, Chuanzeng Zhang
Summary: This paper provides an overview of the singular boundary method (SBM) and its various engineering applications. It introduces the basic concepts of SBM and classifies the approaches for determining origin intensity factors. It also presents additional schemes to resolve non-uniqueness issues and highlights future trends in this research field.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Mathematics, Applied
Suifu Cheng, Fajie Wang, Po-Wei Li, Wenzhen Qu
Summary: A novel Burton-Miller-type singular boundary method (BM-SBM) is proposed in this paper for acoustic design sensitivity analysis. Compared with traditional methods, this approach is accurate, semi-analytical, and meshless, and it can effectively address the exterior Helmholtz problems encountered in acoustic design.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Physics, Mathematical
Ignacio Labarca, Ralf Hiptmair
Summary: Time-domain acoustic scattering problems in two dimensions are studied using Convolution Quadrature (CQ) method and method of fundamental solutions (MFS), which efficiently and accurately solve frequency-domain Helmholtz equations with complex wavenumbers for exterior and interior problems.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Xiaoguang Yuan, Quan Jiang, Zhidong Zhou, Fengpeng Yang
Summary: This paper extends the method of fundamental solutions (MFS) for solving the boundary value problems (BVPs) of analytic functions. The conformal mapping technique is applied to introduce singularities and reconstruct the fundamental solutions. The proposed method has the advantages of conciseness, reliability, efficiency, high accuracy, and easy-using.
Article
Engineering, Multidisciplinary
Yao Sun, Xinru Lu, Bo Chen
Summary: This paper introduces the method of fundamental solutions for the 2D high frequency acoustic-elastic interaction problem and explores its relationship with a pure acoustic problem. Displacements are approximated using the linear combination of fundamental matrix tensors of the Navier equation, while the acoustic scattered field outside the elastic solid is approximated using the linear combination of fundamental solutions of the Helmholtz equation. Real data examples are provided, including copper alloy in water, oil, cork wood, and air. The accuracy of the method is validated using an exact solution in the first example, and it is found that the acoustic-elastic interaction problem approaches a pure acoustic problem with a sound-hard boundary as the density ratio of the two mediums increases.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Guizhong Xie, Rongjie Huang, Yunqiao Dong, Hao Li, Ke Li, Yudong Zhong, Xiaoyun Gong, Wenliao Du, Liangwen Wang
Summary: This paper presents an accurate computation method for stress intensity factors (SIFs) of two-dimensional cracks using an interaction integral method combined with special crack tip elements. The method considers the special variation of displacement around the crack tip and applies a general method for singular integrals and nearly singular integrals. The effectiveness of the proposed method is demonstrated through numerical examples.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Mathematics, Applied
David B. Stein, Alex H. Barnett
Summary: Well-conditioned boundary integral methods are powerful tools for static and dynamic physical simulations. Evaluating nearly singular integrals becomes highly efficient by precomputing a linear map from surface density to an effective source representation.
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Shuainan Liu, Po-Wei Li, Chia-Ming Fan, Yan Gu
Summary: This paper explores the use of LMFS for numerically solving general transient convection-diffusion-reaction equations in 2D and 3D materials. The method utilizes CN time-stepping technology and CCS approximation for solving boundary value problems efficiently.Various benchmark examples demonstrate the effectiveness and feasibility of the approach compared to traditional methods like MFS and BEM.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Mathematics
Weiwei Li, Fajie Wang
Summary: This paper presents a precorrected-FFT accelerated singular boundary method (pFFT-SBM) for high-frequency acoustic radiation and scattering problems. The new pFFT-SBM overcomes the limitation of the original method in computational efficiency by introducing a pFFT scheme.
Article
Engineering, Multidisciplinary
Yan Gu, Linlin Sun
Summary: The study introduces an effect boundary element method for electroelastic analysis of ultrathin piezoelectric films/coatings, successfully addressing nearly singular integrals and avoiding the need for remeshing procedures. The method shows promising results in modeling multiple ultrathin piezoelectric films with a relative thickness as low as 10(-8).
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Mathematics, Applied
Xing Wei, Wenjun Luo
Summary: This study introduces a novel two-and-a-half-dimensional (2.5D) singular boundary method (SBM) to solve three-dimensional acoustic problems, which effectively decomposes the problem into simpler 2D problems and proposes a new numerical integration formulation for result interpretation.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Computer Science, Interdisciplinary Applications
Wenzhen Qu, Linlin Sun, Po-Wei Li
Summary: The localized method of fundamental solutions is a recent meshless collocation method that uses fundamental solutions as radial basis functions, forming a sparse system matrix for higher efficiency. A modified version for bending analysis of thin elastic plates introduces auxiliary nodes on the boundary to provide additional weight coefficients, improving the system construction and avoiding over-determination. Numerical experiments show good agreement with analytical solutions.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics, Applied
Linlin Sun, Zhikang Chen, Suyu Zhang, Liu Chu
Summary: This paper extends the wave based method to solve two-dimensional anisotropic elastic wave problems by introducing a new approach to address the lack of basis functions. The accuracy and efficiency of the method are validated through two examples.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Crystallography
Xing Wei, Dongdong Liu, Shuohui Yin
Summary: An effective free vibration optimization procedure using the isogeometric approach, particle swarm optimization, and integrated global and local parameterization is proposed in this paper. The method calculates the natural frequency of functionally graded plates and optimizes the volume fractions of the control points. Numerical examples are provided to demonstrate the reliability and effectiveness of the proposed approach.
Article
Engineering, Multidisciplinary
Xing Wei, Dongdong Liu, Wenjun Luo, Shenshen Chen, Linlin Sun
Summary: The singular boundary method (SBM) is extended to simulate the dynamic response of half-space saturated soils in the frequency domain in this study. The SBM utilizes the fundamental solutions as basis functions and discretizes the domain of interest into several source points on the boundary, allowing for wave propagation description in the half-space soil medium. The source singularity issue is resolved using origin intensity factors (OIFs) for open boundaries, and the feasibility and advantages of the proposed SBM are demonstrated in two numerical examples.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Mathematics
Hui Zheng, Xiaoling Lai, Anyu Hong, Xing Wei
Summary: A novel radial basis function collocation method (RBFCM) using fictitious centre nodes is proposed to solve two-dimensional elastic problems. Compared with the traditional method, this approach has reduced sensitivity to shape parameters, improving stability and accuracy.
Article
Mathematics, Applied
Linlin Sun, Zhuojia Fu, Zhikang Chen
Summary: This paper presents a localized collocation solver for 3D elastic wave propagation analysis based on fundamental solutions. The proposed solver represents the approximated solution at a node by combining the solutions at nearby nodes, resulting in sparse resultant matrix and avoiding ill-conditioned dense matrix commonly encountered in collocation methods. The efficiency and accuracy of the method have been verified through benchmark examples.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Zhikang Chen, Linlin Sun
Summary: This work develops the boundary knot method (BKM) for 2D coupled thermoelasticity problems in the frequency domain. The BKM does not require domain discretization and is formulated in terms of discretized boundary points. The non-singular general solution is derived using Helmholtz decomposition and eigen-analysis. The accuracy and feasibility of the proposed method are demonstrated through numerical examples.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Xing Wei, Chengliang Rao, Shenshen Chen, Wenjun Luo
Summary: This paper presents a semi-analytical boundary meshless method called the singular boundary method (SBM) to simulate anti-plane wave motion in heterogeneous media. Two different continuous inhomogeneity variations are studied, and the corresponding fundamental solutions are derived through a simple variable transformation. The fundamental solutions, determined by the wavenumbers of the governing equations after the variable transformation, overcome the source singularities with the help of novel origin intensity factors (OIFs). The SBM is demonstrated to be effective for simulating anti-plane wave scattering and diffraction in nonhomogeneous media through numerical experiments.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Engineering, Multidisciplinary
Weiwei Li, Linlin Sun, Yan Gu, Fajie Wang
Summary: In this study, the singular boundary method is employed to calculate the band structures of in-plane waves in two-dimensional phononic crystals. The method discretizes the whole boundaries and derives a linear eigenvalue equation, providing stable and efficient results for band structure calculations.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Review
Engineering, Multidisciplinary
Zhuojia Fu, Qiang Xi, Yan Gu, Junpu Li, Wenzhen Qu, Linlin Sun, Xing Wei, Fajie Wang, Ji Lin, Weiwei Li, Wenzhi Xu, Chuanzeng Zhang
Summary: This paper provides an overview of the singular boundary method (SBM) and its various engineering applications. It introduces the basic concepts of SBM and classifies the approaches for determining origin intensity factors. It also presents additional schemes to resolve non-uniqueness issues and highlights future trends in this research field.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Mathematics
Dongdong Liu, Xing Wei, Chengbin Li, Chunguang Han, Xiaxi Cheng, Linlin Sun
Summary: In this paper, the singular boundary method (SBM) in conjunction with the exponential window method (EWM) is extended to simulate the dynamic response of two-dimensional saturated soil. The SBM solves the governing equations in the frequency domain using a linear combination of fundamental solutions. The EWM is used for inverse Fourier transform to obtain time domain solutions. The results demonstrate that the SBM-EWM method is accurate and feasible for analyzing the transient behavior of saturated soil.
Article
Engineering, Multidisciplinary
A. A. Aganin, A. I. Davletshin
Summary: A mathematical model of interaction of weakly non-spherical gas bubbles in liquid is proposed in this paper. The model equations are more accurate and compact compared to existing analogs. Five problems are considered for validation, and the results show good agreement with experimental data and numerical solutions. The model is also used to analyze the behavior of bubbles in different clusters, providing meaningful insights.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Hao Wu, Jie Sun, Wen Peng, Lei Jin, Dianhua Zhang
Summary: This study establishes an analytical model for the coupling of temperature, deformation, and residual stress to explore the mechanism of residual stress formation in hot-rolled strip and how to control it. The accuracy of the model is verified by comparing it with a finite element model, and a method to calculate the critical exit crown ratio to maintain strip flatness is proposed.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Shengwen Tu, Naoki Morita, Tsutomu Fukui, Kazuki Shibanuma
Summary: This study aimed to extend the finite element method to cope with elastic-plastic problems by introducing the s-version FEM. The s-version FEM, which overlays a set of local mesh with fine element size on the conventional FE mesh, simplifies domain discretisation and provides accurate numerical predictions. Previous applications of the s-version FEM were limited to elastic problems, lacking instructions for stress update in plasticity. This study presents detailed instructions and formulations for addressing plasticity problems with the s-version FEM and analyzes a stress concentration problem with linear/nonlinear material properties.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Bo Fan, Zhongmin Wang
Summary: A 3D rotating hyperelastic composite REF model was proposed to analyze the influence of tread structure and rotating angular speed on the vibration characteristics of radial tire. Nonlinear dynamic differential equations and modal equations were established to study the effects of internal pressure, tread pressure sharing ratio, belt structure, and rotating angular speed on the vibration characteristics.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
X. W. Chen, Z. Q. Yue, Wendal Victor Yue
Summary: This paper examines the axisymmetric problem of a flat mixed-mode annular crack near and parallel to an arbitrarily graded interface in functionally graded materials (FGMs). The crack is modeled as plane circular dislocation loop and an efficient solution for dislocation in FGMs is used to calculate the stress field at the crack plane. The analytical solutions of the stress intensity factors are obtained and numerical study is conducted to investigate the fracture mechanics of annular crack in FGMs.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Xumin Guo, Jianfei Gu, Hui Li, Kaihua Sun, Xin Wang, Bingjie Zhang, Rangwei Zhang, Dongwu Gao, Junzhe Lin, Bo Wang, Zhong Luo, Wei Sun, Hui Ma
Summary: In this study, a novel approach combining the transfer matrix method and lumped parameter method is proposed to analyze the vibration response of aero-engine pipelines under base harmonic and random excitations. The characteristics of the pipelines are investigated through simulation and experiments, validating the effectiveness of the proposed method.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Xiangyu Sha, Aizhong Lu, Ning Zhang
Summary: This paper investigates the stress and displacement of a layered soil with a fractional-order viscoelastic model under time-varying loads. The correctness of the solutions is validated using numerical methods and comparison with existing literature. The research findings are of significant importance for exploring soil behavior and its engineering applications under time-varying loads.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Thuy Dong Dang, Thi Kieu My Do, Minh Duc Vu, Ngoc Ly Le, Tho Hung Vu, Hoai Nam Vu
Summary: This paper investigates the nonlinear torsional buckling of corrugated core sandwich toroidal shell segments with functionally graded graphene-reinforced composite (FG-GRC) laminated coatings in temperature change using the Ritz energy method. The results show the significant beneficial effects of FG-GRC laminated coatings and corrugated core on the nonlinear buckling responses of structures.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Zhihao Zhai, Chengbiao Cai, Qinglai Zhang, Shengyang Zhu
Summary: This paper investigates the effect of localized cracks induced by environmental factors on the dynamic performance and service life of ballastless track in high-speed railways. A mathematical approach for forced vibrations of Mindlin plates with a side crack is derived and implemented into a train-track coupled dynamic system. The accuracy of this approach is verified by comparing with simulation and experimental results, and the dynamic behavior of the side crack under different conditions is analyzed.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
James Vidler, Andrei Kotousov, Ching-Tai Ng
Summary: The far-field methodology, developed by J.C. Maxwell, is utilized to estimate the effective third order elastic constants of composite media containing random distribution of spherical particles. The results agree with previous studies and can be applied to homogenization problems in other fields.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Kim Q. Tran, Tien-Dat Hoang, Jaehong Lee, H. Nguyen-Xuan
Summary: This study presents novel frameworks for graphene platelets reinforced functionally graded triply periodic minimal surface (GPLR-FG-TPMS) plates and investigates their performance through static and free vibration analyses. The results show that the mass density framework has potential for comparing different porous cores and provides a low weight and high stiffness-to-weight ratio. Primitive plates exhibit superior performance among thick plates.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Bence Hauck, Andras Szekrenyes
Summary: This study explores several methods for computing the J-integral in laminated composite plate structures with delamination. It introduces two special types of plate finite elements and a numerical algorithm. The study presents compact formulations for calculating the J-integral and applies matrix multiplication to take advantage of plate transition elements. The models and algorithms are applied to case studies and compared with analytical and previously used finite element solutions.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Wu Ce Xing, Jiaxing Wang, Yan Qing Wang
Summary: This paper proposes an effective mathematical model for bolted flange joints to study their vibration characteristics. By modeling the flange and bolted joints, governing equations are derived. Experimental studies confirm that the model can accurately predict the vibration characteristics of multiple-plate structures.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Pingchao Yu, Li Hou, Ke Jiang, Zihan Jiang, Xuanjun Tao
Summary: This paper investigates the imbalance problem in rotating machinery and finds that mass imbalance can induce lateral-torsional coupling vibration. By developing a model and conducting detailed analysis, it is discovered that mass imbalance leads to nonlinear time-varying characteristics and there is no steady-state torsional vibration in small unbalanced rotors. Under largely unbalanced conditions, both resonant and unstable behavior can be observed, and increasing lateral damping can suppress instability and reduce lateral amplitude in the resonance region.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Yong Cao, Ziwen Guo, Yilin Qu
Summary: This paper investigates the mechanically induced electric potential and charge redistribution in a piezoelectric semiconductor cylindrical shell. The results show that doping levels can affect the electric potentials and mechanical displacements, and alter the peak position of the zeroth-order electric potential. The doping level also has an inhibiting effect on the first natural frequency. These findings are crucial for optimizing the design and performance of cylindrical shell-shaped sensors and energy harvesters.
APPLIED MATHEMATICAL MODELLING
(2024)
